The time-of-flight mass spectrometer (which is hereinafter referred to as a “TOFMS”) is a device for calculating the mass-to-charge ratio of an ion using the fact that the flying speed of an accelerated ion varies depending on the mass-to-charge ratio of the ion. In this device, ions are made to fly a predetermined distance, the time of flight (or “which is appropriately referred to as the “flight time” in this specification) of each of the ions during their flight is measured, and the mass-to-charge ratio of each ion is computed from the flight time. In the TOFMS, since the flying speed of an ion depends on the amount of initial energy given from an electric field or the like, the flight time of each ion has energy dependency. As a result, the initial energy width of an ion packet (a group of ions with the same mass-to-charge ratio) affects the mass-resolving power of the device. Therefore, improving the energy-focusing property of the flight time of the ion is one of the major problems to be solved for improving the performance of the TOFMS.
A commonly known, effective solution to the previously described problem is the use of a reflectron capable of the energy-focusing of the flight time by reflecting ions by a reflecting electric field. In the reflectron, for a group of ions having the same mass-to-charge ratio, an ion with a higher energy (and hence a higher speed) penetrates more deeply into the reflecting electric field and turns around, thus covering a longer traveling path (flight distance). This difference in the traveling length corrects the error in the flight time associated with the variation in the amount of initial energy of the ions and thereby improves the energy-focusing property of the flight time. Reflecting the ions by the reflectron is also effective for providing a longer flight distance without increasing the entire size of the device. For a TOFMS, a longer flight distance gives a higher mass-resolving power. Thus, the use of a reflectron is advantageous in that the mass-resolving power can be improved while suppressing the size and cost of the device.
The simplest structure of the reflectron is a single-stage reflectron, which uses one uniform decelerating electric field of an even field strength. Unfortunately, the single-stage reflectron cannot achieve a sufficiently high level of energy-focusing property of the flight time. Therefore, a two-stage reflectron is commonly used in recent years, which employs the combination of two modes of uniform decelerating electric fields as the reflecting electric field, with the second-stage electric field being designed to repel ions (see Non-Patent Document 1). The combination of the two uniform decelerating electric fields allows the two-stage reflectron to appropriately adjust its dimensions (e.g. length) and the strengths of the two fields so as to achieve a higher level of energy-focusing property of the flight time than that of the one-stage reflectron. Therefore, almost all the commercially available TOFMSs use two-stage reflectrons to create a system that is simple structured and yet can achieve a relatively high performance.
An approach for improving the energy-focusing property of the flight time in a conventional TOFMS having the previously described configuration is hereinafter schematically described.
As already explained, the flight time of an ion has energy dependency since the speed of an ion injected into the flight space of a TOFMS normally depends on the initial energy. In conventional TOFMSs, the flight time of an ion is expressed in the form of a series expansion with respect to the initial energy of the ion in order to evaluate the energy dependency of the flight time in the stage of theoretical design. Consider the case where, for a given type of TOFMS, U denotes the initial energy of an ion with mass m and charge number z, and U0 and T0 respectively denote the reference value of the initial energy and that of the flight time for the same kind of ions (having the same mass and charge number). Under these conditions, the flight time T0 will be a function including device dimensions as constant factors and having the mass-to-charge ratio m/z of the ion as a variable. On the other hand, the flight time T of an ion having an arbitrary amount of initial energy U will be expressed as the following equation (1) using the flight time T0 of the reference ion and the reference initial energy U0:
                    T        =                              T            0                    +                                    T              1                        ⁡                          (                                                U                  -                                      U                    0                                                                    U                  0                                            )                                +                                                    T                2                            ⁡                              (                                                      U                    -                                          U                      0                                                                            U                    0                                                  )                                      2                    +                                    T              3                        ⁡                          (                                                U                  -                                      U                    0                                                                    U                  0                                            )                                +          …                                    (        1        )            
Equation (1) is a series expansion representing the flight time as a sum of powers of the ratio of the energetic displacement to the energy of the reference ion. The coefficient T1, T2, . . . of the term of each order of the expansion is called a flight-time aberration coefficient, which is expressed by using device parameters, such as the device dimensions or voltage conditions. For this expression, one method for reducing the energy dependency of the flight time is, as in the case of the existing aberration theory, to adjust the device parameters so that as many of the aberration coefficients as possible from the lowest-order term through the higher-order terms will be zero. For example, in the previously described two-stage reflectron using two-stage uniform decelerating electric fields, it is possible to appropriately adjust the lengths and strengths of the two uniform decelerating electric fields so as to zero the aberration coefficients up to the second order, thus achieving the second-order energy focusing. However, the third and higher-order aberration coefficients of the two-stage reflectron are not zero, and there remains some energy dependency due to these coefficients. Therefore, when the initial energy width of the ions is large, the observed flight-time peak will be significantly broadened and the mass-resolving power will be low.
Another example is a method proposed in Patent Document 1, in which the energy dependency of the flight time of the ion within the reflecting electric field is completely eliminated by increasing the field strength in the reflecting electric field in proportion to the penetration depth of the ion, i.e. by creating a parabolic potential distribution on the ion-beam axis, to make the motion of each ion a simple harmonic motion. In principle, the energy dependency of the flight time can be completely eliminated by this method. However, in practice, its performance cannot be fully exploited if the device does not satisfy a difficult structural requirement: the starting point of the ions and the detector must be located on the boundary of the reflecting electric field. To address this problem, a method has been proposed in Patent Document 2, in which the function form of the strength distribution of the reflecting electric field is changed so that an energy-focusing property of the flight time comparable to that of the one-stage reflectron can be achieved over a broader range of energy even if the starting point of the ions and the detector are separated from the reflecting electric field by a free space.
In recent years, mass spectrometers, including TOFMSs, have come to be used to analyze a wider variety of substances having more complicated structures than ever before. The demands for further improvements in the performances of the measurement, such as the accuracy, sensitivity and resolving power, have also become stronger. Despite the various innovative ideas applied thereto, the previously described conventional TOFMSs cannot achieve a sufficiently high energy-focusing property of the flight time to meet the aforementioned requirements. With an increase in the initial energy width of the ions, the observed peak width of the flight time also increases, lowering the mass resolving power. Accordingly, to achieve a high mass-resolving power, it is necessary to take some measures to reduce the initial energy width of the ions in the source from which ions are released. However, such measures have certain limitations. Thus, enhancing the energy-focusing property of the flight time in the flight space including a reflectron is very important to improve the mass-resolving power of the TOFMS.